Problem: Gabriela is 16 years older than Jessica. For the last two years, Gabriela and Jessica have been going to the same school. Thirteen years ago, Gabriela was 3 times older than Jessica. How old is Gabriela now?
Answer: We can use the given information to write down two equations that describe the ages of Gabriela and Jessica. Let Gabriela's current age be $g$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $g = j + 16$ Thirteen years ago, Gabriela was $g - 13$ years old, and Jessica was $j - 13$ years old. The information in the second sentence can be expressed in the following equation: $g - 13 = 3(j - 13)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $g$ , it might be easiest to solve our first equation for $j$ and substitute it into our second equation. Solving our first equation for $j$ , we get: $j = g - 16$ . Substituting this into our second equation, we get the equation: $g - 13 = 3($ $(g - 16)$ $ -$ $ 13)$ which combines the information about $g$ from both of our original equations. Simplifying the right side of this equation, we get: $g - 13 = 3g - 87$ Solving for $g$ , we get: $2 g = 74$ $g = 37$.